A Study of stable wormhole solution with non-commutative geometry in the framework of linear $f(R,\mathcal{L}_m, T)$ gravity

TL;DR

This paper investigates stable traversable wormhole solutions within a modified gravity framework incorporating non-commutative geometry, analyzing energy conditions, gravitational lensing effects, and stability criteria for different matter coupling parameters.

Contribution

It introduces a novel analysis of wormholes in linear $f(R, ext{L}_m,T)$ gravity with non-commutative geometry, deriving shape functions and stability conditions for the first time.

Findings

Exotic matter is required for positive couplings to violate NEC.

Negative couplings can avoid exotic matter under specific bounds.

Gravitational lensing indicates repulsive gravity effects for large negative couplings.

Abstract

This research delves into the potential existence of traversable wormholes (WHs) within the framework of modified, curvature based gravity. The modification includes linear perturbations of the matter Lagrangian and the trace of the energy-momentum tensor with specific coupling strengths $\alpha$ and $\beta$ and can thus be viewed as a special case of linear $f(R,T)$-gravity with a variable matter coupling or as the simplest additively separable $f(R,\mathcal{L}_m,T)$-model. A thorough examination of static WH solutions is undertaken using a constant redshift function; therefore, our work can be regarded as the first-order approximation of WH theories in $f(R,\mathcal{L}_m,T)$ . The analysis involves deriving WH shape functions based on non-commutative geometry, with a particular focus on Gaussian and Lorentzian matter distributions $\rho$. Constraints on the coupling parameters are developed so that the shape function satisfies both the flaring-out and asymptotic flatness conditions. Moreover, for positive coupling parameters, violating the null energy condition (NEC) at the WH throat $r_0$ demands the presence of exotic matter. For negative couplings, however, we find that exotic matter can be avoided by establishing the upper bound $\beta+\alpha/2<-\frac{1}{\rho r_0^2}-8\pi$. Additionally, the effects of gravitational lensing are explored, revealing the repulsive force of our modified gravity for large negative couplings. Lastly, the stability of the derived WH solutions is verified using the Tolman-Oppenheimer-Volkoff (TOV) formalism.